Robust Partial Quadratic Eigenvalue Assignment Problem: Spectrum Sensitivity Approach

TL;DR

This paper introduces a robust optimization method for the partial quadratic eigenvalue assignment problem in vibration control, utilizing sensitivity-based cost functions and efficient algorithms that avoid eigenvector computations.

Contribution

It presents a novel sensitivity-based cost function and explicit gradient formulas for solving the robust partial quadratic eigenvalue assignment problem efficiently.

Findings

Algorithms demonstrate high efficiency and robustness.

Compared favorably with existing methods in numerical experiments.

Effective for both state feedback and derivative feedback designs.

Abstract

We propose an optimization approach to the solution of the partial quadratic eigenvalue assignment problem (PQEVAP) for active vibration control design with robustness (RPQEVAP). The proposed cost function is based on the concept of sensitivities over the sum and the product of the closed-loop eigenvalues, introduced recently in our paper. Explicit gradient formula for the solutions using state feedback and derivative feedback are derived as functions of a free parameter. These formulas are then used to build algorithms to solve RPQEVAP in a numerically efficient way, with no need to compute new eigenvectors, for both state feedback and state-derivative feedback designs. Numerical experiments are carried out in order to demonstrate the effectiveness of the algorithms and to compare the proposed method with other methods in the literature, thus showing its effectiveness.